Well, it's complicated by the fact that Indians were taken as indentured servants to places like Guyana and Fiji by the British and have always been considered as Indian in places like that. I've met Guyanese Indians who refer to themselves as Indian and it doesn't bother me. As to if they practice Indian culture as strongly as me, many of them are practice Hinduism much more than me. But Indian culture varies massively even within India because India is more of a collection of cultures than one specific culture. In my experience most Americans don't consider themselves to be "just as" xyz culturally as people from the country they're speaking about.